Are there any differences between private and non-private back operation patients

private and non-private back operation patients

Author: Deliang Dai Supervisor: Adam Taube

Part of the fulfillment of the requirements for the degree of master of Statistics, June 2010

1

Abstract

It has been claimed that there are considerable differences between pri- vate and non-private patients with regard to the outcome of back surgery.

This can be found in the yearly report from the register concerning back

surgery in Sweden. However, the results seem doubtful and the references

could not be found. Therefore, we analyze the data about nearly 1200

patients from the clinic of back surgery in Str¨ angn¨ as (CSS). It includes

three time periods with somewhat different questionnaires from 1986 to

2007 with both private and non-private patients. In the third period,

the patients have been evaluated using the SF-36 questionnaire. The re-

sults show that most of the differences between private and non-private

patients are minor and not statistically significant.

CONTENTS 3

Contents

1 Introduction 4

1.1 Available data sets . . . . 5 2 Basic facts concerning private and non-private patients 7

3 Patients’ attitudes in subpopulation 3 15

3.1 Analysis of the summary score . . . . 17 3.2 Svensson’s method . . . . 18 3.3 The difference of differences . . . . 23

4 Conclusions 26

4.1 Conclusions for all three subpopulations . . . . 26 4.2 Conclusions for subpopulations 3 . . . . 26

A Guideline to the figures 30

B Details of questionnaires in the subpopulations 32

C The SF-36 questionnaire 36

D The missing response rate of SF-36 40

E The ROC curves of patients’ attitudes in subpopulation 3 41

1 Introduction

At present, there is a big interest in Sweden for comparisons of the outcome between different medical units. A number of medical registers have been created and results from various clinics are being compared on the basis of outcome data from these registers. However, a comparison between different clinics does not only reflect the effectiveness at these units but is also influ- enced by the so called patient mix.

In the discussion of results from the clinic of back surgery in Str¨ angn¨ as (CSS), it has been pointed out that the results from this clinic are not directly com- parable with those from other clinics due to the fact the Str¨ angn¨ as clinic has a considerable fraction of private patients. The private patients, as the name implies, are the patients who paid the operation fee by themselves.

The term “private” in this thesis includes patients who pay their operation themselves, those who have a private insurance paying the operation and also those whose operations are paid by their employer. On the other hand, the “non-private” means the patients whose operation was paid totally by general insurance or county.

In the yearly report (ref[7]) from the register concerning back surgery in Sweden, it is stated that “most international studies show obvious differ- ences between private patients and non-private patients with regard to the results from back surgery and it can be expected that the circumstances are the same in Sweden”. It appears however that this statements is false and the references referred to can not be found. Therefore it is of great interest to investigate whether differences between these two patient categories really do exist.

Here we will not make any comparison between the results from CSS with any other clinics, but since there has been both private and non private patients at CSS, we have the possibility to compare these two categories within CSS in order to answer the question: Are there any differences between private and non-private patients?

On the basis of data concerning a number of patients operated upon with

regard to lumbar disc herniation (LDH), we will investigate in more detail

these possible differences. Patients with lumbar disc herniation (LDH) gen-

erally present with some pain in the back but above all with pain radiating

down one of the legs due to nerve root compression. Sometimes there is also

numbness and tingling sensations in the same area. The leg pain is often

1 INTRODUCTION 5

pronounced and might prevent the patient from working.

1.1 Available data sets

It appears that we can get rather detailed data concerning the actual patients for the period 1986 to 2007 during which nearly 1200 patients were operated upon.

Table 1: The basic table about population

Subpopulation Period Sample size Way of payment

1 1986 - 1996 493 Private=428 (88.84%)/ Non-pri=65 (11.16%) 2 1997 - 1999 208 Private=177 (85.17%)/ Non-pri=31 (14.83%) 3 2000 - 2007 483 Private=132 (27.33%)/ Non-pri=351 (72.67%)

Figure 1 The period of phases and their corresponding sample sizes.

For several reasons it is feasible to divide this population into 3 subpopula- tions:

First, during the actual time, more and more variables and questions have been included. From the tables in appendix we see that the variables in sub- population 2 and subpopulation 3 are more detailed than in subpopulation 1.

As the question: what do you think of the results of the DH operation? The

intersection variables of these 3 subpopulation are limited. Hence, dividing

the time period gives a better way to analyze our data.

Second, there are some questions which were given only in the subpopulation 1. For instance, the SRS (segmental pain). And the ways of payment have been specified differently in different time periods below in table 2.

Third, a more specialized questionnaire with a great number of items was applied on subpopulation 3.

Table 2 The table about the payment ways in three subpopulation.

In subpopulation 1, the category “some sort of insurance” had a special way of payment which was a kind of farmer insurance. The farmers who paid the operation via this insurance were also shareholders of CSS. As the time passed, this way of payment disappeared in subpopulation 2. On the other hand, the “other” category is a payment way for the staff in CSS. As a result, these two ways of payment are referred to the private patients.

From table 2 we can see that the payment ways are different between subpop- ulation 1 and subpopulation 2,3. In subpopulation 1, there are 7 payment ways where the first two ones are “non-private” and the last five ones are

“private”. In subpopulation 2 and 3, beside the “non-private” one, the others

are all private patients. The sample sizes are given in the table as well. As

time passed, the number of non-private patients increased and the number

of private patients decreased.

2 BASIC FACTS CONCERNING PRIVATE AND NON-PRIVATE PATIENTS7

As mentioned before, we are concerned with the difference between the pri- vate and non-private patients at CSS. In our data set, there are several categories which could be included in the category under the label “private payment”. For instance, beside the “private” category, the “company” and

“insurance company” belong to private patients, since these institutions paid the DH operation fees for the patients because the patients had handed in fixed amount of money to the institution at regular intervals. It’s an indirect payment way by itself. On the other hand, the non-private patients are the patients for which the operation fees are totally paid by county or general insurance in Sweden.

It’s more convenient to include results from these three subpopulation in one figure when it is possible. However, since the time span of the data col- lection is long (1986-2007), the formats of the questionnaires have changed somewhat. As we said before, the answers of the question are changed from dichotomous to ordinal or nominal variables sometimes.

We will first present the results concerning those variables that can be found in similar form for all three subpopulation.

2 Basic facts concerning private and non-private patients

[AGE] There is quite a large variability in age among the patients - the

youngest one was 15 years old and the oldest was 79 years old and the mean

age for all of them was 42.76 years old. (S.D. = 10.28 years), the cumula-

tive density functions of age for patients with different ways of payment are

illustrated in figure 2.

Figure 2 The cumulative density functions of age.

From table 3 we can see that there are only minor differences between private and non-private patients. In fact, the differences are non-significant. How- ever we notice that the patients in subpopulation 3 are somewhat older

Table 3 The basic table about age

Age mean S.D Sample size Age range

Private(Subpopulation 1) 42.9 10.04 428 (17,79) Non-private(Subpopulation 1) 41.85 11.83 65 (15,68) Private(Subpopulation 2) 42.54 10.59 177 (17,72) Non-private(Subpopulation 2) 42.12 13.29 31 (18,63) Private(Subpopulation 3) 44.29 11.36 132 (17,72) Non-private(Subpopulation 3) 43.53 12.07 351 (20,78)

[GENDER]:From figure 3, overall, it can be seen that there are more males

than females in each of all the three subpopulations and we notice that there

are slightly more males among the non-private patients than private patients

in all 3 subpopulations. The difference in subpopulation 2 is significant.

2 BASIC FACTS CONCERNING PRIVATE AND NON-PRIVATE PATIENTS9

Figure 3 The basic figure of gender.

[DH RELATION] In figure 4, the proportions of patients who had got their attack of DH “related to a special event” are roughly equal for private and non-private patients. The differences are not significant here even for sub- population 2.

Figure 4 The basic figure of patients get DH related to a special reason.

In the following figures 5-7 and 10-11, each subpopulation is represented with

a dotted line. If this line coincides with the diagonal, there is no difference

between private and non-private patients. If the curve is above the diagonal,

the private patients are better off than the non-private patients. If the curve

is below the diagonal, the opposite is true. The larger the area between

the curve and the diagonal is, the larger is the difference between private

and non-private patients. The diagonal represents the null alternative: no

difference between private and non-private patients. For further details see

appendix

.

[LUMBAR PAIN] In subpopulation 1, this question is dichotomous with 88.34% of private patients having lumbar pain and 92.19% for non-private patients. The curves in figure 5 represent subpopulation 2 and 3. Figure 5 shows different directions for subpopulation 2 and 3. In subpopulation 2, the non-private patients have a better situation than the private patients while the opposite is true in subpopulation 3. The area between the curve and di- agonal of subpopulation 2 seems equal subpopulation 3. However we notice that the number of patients is small in subpopulation 2 and only in sub- population 3 there is a significant difference between private and non-private patients. Thus, concerning lumbar pain, there is no clear picture concerning the difference between private and non-private patients.

Figure 5 The basic figure of lumbar pain before operation.

[SICK LEAVE] In figure 6, we have a similar situation as in figure 5. The question for subpopulation 1 is dichotomous with 99.3% “yes”for private pa- tients who asked sick leave because of DH reason and 96.8% for non-private patients. From figure 6, we can see that the differences between private and non-private patients are negligible in both subpopulation 2 and 3.

1

For understanding the thesis easier, we explain more details of the figures in Appendix

A

2 BASIC FACTS CONCERNING PRIVATE AND NON-PRIVATE PATIENTS11

Figure 6 The basic figure of sick leave because of DH.

[PHYSICALWORK] In subpopulation 1, the answer options were different

for the question “How much physical work was related to your job before you

had the OP? ” compared with subpopulation 2 and 3. It is an ordinal variable

with options: “sitting all the time”, “still” and “changing”. In fact, the first

two options “sitting all the time” and “still” have a similar meaning. There

are 78.69% non-private patients who did a non-physical work while there are

64.29% for private patients. The differences are nonsignificant. From figure

7 we can see that there are somewhat more non-private patients who did a

physical work in both subpopulation 2 and 3.

Figure 7 The basic figure of type of work.

[DURATION] From figure 8, it is obvious that the difference between the private and non-private patients in durations of symptom is minor in subpop- ulation 1, even if the non-private patients have a somewhat longer symptoms duration.

Figure 8 The density functions of symptoms duration.

From table 4, it can be seen that the private patient’s symptoms duration de- creased as time passed while the non-private patient’s remained on the same level. In subpopulation 3, the difference between private and non-private is highly significant with p< 0.001. It’s a noticeable phenomenon because the symptoms duration is of importance for the further success with the opera- tion.

Table 4 The basic table about symptoms duration in month

Duration mean S.D Sample size Range Duration ≥ 48 Private(Subpopulation 1) 8.9 12.81 428 (0.25,120) 10 Private(Subpopulation 2) 7.83 8.47 177 (0.25,50) 3

Private(Subpopulation 3) 6.27 6.49 132 (0.5,60) 1

Non-private(Subpopulation 1) 10.1 10.98 65 (0.25,48) 2 Non-private(Subpopulation 2) 10.94 14.76 31 (1,84) 1 Non-private(Subpopulation 3) 10.01 16.08 351 (0.25,186) 10

[LEG PAIN] Figure 9 shows a somewhat better recovery concerning leg pain

among private patients in all three subpopulations, however not statistically

significant. It might be so due to the fact that private patients have shorter

2 BASIC FACTS CONCERNING PRIVATE AND NON-PRIVATE PATIENTS13

symptoms duration than non-private patients. The leg pain is an important indicator for patient recovery since in disc herniation the nerve root can be compressed too long, compression might delay and even prevent recovery.

Therefore leg pain reflects the recovery situation.

[BACK PAIN]In figure 10, the back pain reveals a similar pattern compared with leg pain for both private and non-private patients.

Figure 9 The basic figure of leg pain after operation.

Figure 10 The basic figure of back pain after operation.

From table 5, it can be seen that there are no noticeable differences concern-

ing “re-operation after operation”.

Table 5 The basic table about re-operation

No Hospital stay 3 months 4 - 12 months 1 year OP, other niveau

nonpri1 87.69% 0 4.62% 3.08% 3.08% 1.54%

private1 92.06% 0.7% 1.64% 1.64% 1.64% 2.34%

nonpri2 96.77% 0 0 0 3.23% 0

private2 89.77% 1.7% 2.84% 1.7% 3.41% 0.57%

nonpri3 90.29% 0.86% 2.29% 3.14% 2.57% 0.86%

private3 90.84 % 0.76% 0 3.05% 5.34% 0

From the results above, we conclude that:

1. There are more males than females among the patients in general. There are also more males among the non-private patients than among the private patients.

2. Among the private patients, lumbar pain was somewhat less common.

However, the difference between the private and non-private patients is not statistically significant.

3. The private patients had shorter symptoms duration. The differences are not statistically significant in subpopulation 1 and subpopulation 2. However, the difference between private and non-private patients is highly significant in subpopulation 3.

It can be several reasons why private patients paid the operation fee them- selves: one might be that they want to have the surgery as quickly as possible, and another that they may be denied an operation in their ordinary hospi- tals. If this is so, it can explain that they had a shorter symptoms duration and less lumbar pain.

4. The difference concerning sick leave between private and non-private pa- tients is negligible.

5. Among the non-private patients, physical work was a little more common.

The difference was not statistically significant however.

Even if we have found some differences between private and non-private pa-

tients, the overall impression is that these differences are quite small and of

minor importance.

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 15

3 Patients’ attitudes in subpopulation 3

In subpopulation 3, besides the questionnaire we mentioned above, CSS used another kind of questionnaire. The “Short Form-36”(SF-36)

was used to evaluate the patients’ attitude and other changes between pre- and post- operation.

The short SF-36 health questionnaire is a common instrument to measure people’s health quality and it is also a part of MOS (Medical Outcome of Study) originated from the RAND

corporation. It contains 36 questions in total, with various ordinal answer categories and 8 summary scores, which gives a profile of the functional health. The structure of SF-36 is given in figure 11.

The table 6 below gives the number of missing response patients in the sub- population 3.

Table 6 The number of missing response patients in subpopulation 3.

Missing type Number of patients Totally missing questionnaire 3

Incomplete questionnaire 141 Completed questionnire 339

It is regrettable that the partial non-response is as large as it is. The missing response rate for the separate questions is given in appendix. For further analysis, we have only used the completed questionnaires.

Even if there is a considerable rate of non-response, it doesn’t seem as there is a differences between private and non-private patients with regard to non- response. This is also the impression from the data concerning the partial non-response rate given in table of appendix D.

1

More details of Short Form 36 are given in appendix

2

Research And Development, see http://www.rand.org/.

Table 7 The scale of the summary scores Physical health Mental health Physical Functioning (PF) Vitality (VT)

Role-Physical (RP) Social Functioning (SF) Bodily Pain (BP) Role-Emotional (RE) General Health (GH) Mental Health (MH)

Table 8 The non-response rate in subpopulation 3.

Type Private Non-Private

Completed 94 245

Totally 132 351

Proportional 71% 70%

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 17

Figure 11 The structure of SF-36.

3.1 Analysis of the summary score

Figure 12 The distribution of the difference between before and after the operation with regard to PCS and MCS.

First of all, we begin with analyzing the summary scores of the physical and mental health. Figure 12 shows the density for two of the difference summary scores between pre- and post-operation for private and non-private patients in physical and mental health. When such difference is larger than 0, the patients has improved. From the shaded areas, we conclude that - on the basics of SF-36 - it can be argued that a great majority of the patients im- proved both physically and mentally after the operation.

However, the focus interest here is whether there were differences between private and non-private patients. For each group, we have studied the dif- ference between before and after the operation. As a further step, we now study the difference between private and non-private patients with regard to the differences

D

− D

= (P

− P

) − (P

− P

)

. Therefore, we can check whether the differences between private and non- private patients are significant by calculating confidence intervals.

From table 9 we can see that the mean difference is not significant in mental health. The difference in physical health is significant however.

Table 9 The confidence interval of difference in summary scores Name mean S.D Confidence interval

Physical health 4.2 1.24 (2.46,6.64) Mental health 2.46 1.53 (-0.53,5.45)

In summary, according to SF-36 summary scores, the patients improved both with regard to physical and mental health. With regard to physical health, the difference between private and non-private is statistical significant.

However the SF-36 is a mixture of ordinal variables which is usually analyzed as a numerical variable as has been done here. This is a somewhat question- able approach. Therefore, we will investigate the differences in the separate items by means of a new statistical method especially intended for this type of data.

3.2 Svensson’s method

It is important to stress that for quality data, the calculation of means, stan- dard deviations as done in 3.1 etc is not appropriate in principle. There are some classical non-parametric methods to handle these kinds of data such as sign test and McNemar’s test. However, they have some limitations, eg:

McNemar is only available for the dichotomous scale.

Therefore, we will apply a new approach which does not contain any inap- propriate mathematical operations. For pedagogical reasons, we start with the situation when the study variable is dichotomous.

In SF-36, there are 7 questions with only two response categories. Consid-

ering the Question 4(c): During the past 4 weeks, were you limited in the

kind of work or other activities?. The actual information was given in two

subgroups for 94 and 245 patients, private and non-private respectively, as

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 19

shown in Table 10 and Table 11. Our point of departure is the null hypoth- esis: there is no difference between pre- and post-operation.

Table 10 Cross tabulation of Question 4(c) for the private patients Post-operation Pre-operation

Total

Yes No

Yes 3 0 3

No 77 14 91

Total 80 14 94

The actual difference between pre- and post-operation answers can be seen from the two marginal distributions.

D

= P

− P

= 80 94 − 3

94 = 0.8191

Noting that 3 patients had problems both before and after the operation and 14 patients had no problem neither before nor after the operation we can write instead

D

= P

− P

= 77 94 − 0

94 = 0.8191

The two proportions are correlated and we get SE(D)=0.0486 (ref[3]) and a 95% confidence interval is 0.8191 ± 1.96 × 0.0397, from 0.7413 to 0.8969. The difference is highly significant. Thus there is an obvious improvement after the operation for the private patients with regard to limitations in their work or other activities.

Table 11 Cross tabulation of Question 4(c) for the non-private patients Post-operation Pre-operation

Total

Yes No

Yes 9 1 10

No 159 76 235

Total 168 78 245

Similarly, the difference concerning the non-private patients is given by D

= P

− P

= 159

245 − 1

245 = 0.6449

And the 95% confidence interval is 0.6449 ± 1.96 × 0.0304, from 0.5853 to 0.7045. Thus there is also a significant improvement among the non-private patients after the operation.

Since our main interest is to investigate whether this kind of difference (pre- operation against post-operation) is different or not between private patients and non-private patients, we will study the “difference of difference”. Thus we get

∆ = D

− D

= 0.8191 − 0.6449 and

s.e(∆) =

s se

n

+ se

n

=

r 0.0397

94 + 0.0304

245 = 0.0044 .

Assuming the ∆ to be normally distributed, we get the confidence interval [0.1698,0.1786]. From this, it is obviously a statistical significant difference between the private and non-private patients with regard to the improvement after the operation with regard to limitations in their work or other activities.

We will now present the same results from above in such way that it is in conformity with the corresponding approach when the actual variable is not dichotomous.

Seen from Table 10 and 11, it is obvious that the discrepancy between the two marginal distributions (the distributions of observations on the ordered categories on the “pre-operation” and “post-operation”) do reflect the gen- eral trend from before to after operation among the patients.

Starting from the horizontal marginal, we observe that the 14 patients with no limitation before the operation, will not be “better” after the operation.

Among the 80 patients who have some limitations before, some might get rid of these limitations after the operation. From the vertical marginal distribu- tion, we see that the probability for “ no limitations” is

. Thus, assuming independence, the probability to get “better” becomes

P

= 80 94

91

94 = 0.8239

Similarly, we can calculate the probability of “to get worse” as P

= 14

94 3

94 = 0.0048

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 21

.

In these calculations, we have only used the marginal frequencies and as- sumed independence. The difference

RP = P

− P

= 0.8239 − 0.0048 = 0.8191

is called the “relative position” and equals the difference which we have pre- viously presented.

Since “RP” is the difference between two probabilities, |RP | ≤ 1 and if the two probabilities are equal (i.e the marginal distributions are identical), RP=0.

The above calculations were based on a dichotomous scale. Quite often, how- ever, it happens that the patients are classified according to an ordinal scale with more than two categories.

It can be shown that the same measure RP = P

− P

can be used even in this situation. Thus having data in a cross-table like table 12 gives a possibility to calculate RP is the measure of the systematic change between

“before” and “after” the operation. This approach was presented by Dr.

Elisabeth Svensson (ref[6]) and there are also possibilities to obtain standard errors for RP. We have applied these methods for all those items in SF-36 which are not dichotomous.The Svensson approach can be further developed to obtain various measures of individual variability, but we have not used that here.

Interpreting table 12 reveals that 26+11+4=41 patients (the diagonal from upper left to lower right) had the same degree of the bodily pain after the operation as before. The cells above the diagonal are the numbers of patients whose bodily pain relieved after the operation. On the contrary, patients who are located below the diagonal got worse instead.

From table 12, we can calculate the RP as the question 7. According to Svensson’s method (ref[7]), we get that

P

=

n

P

i=1

[y

C(X)

]

=

(26 × 74 + 59 × 221 + 39 × 326 + 75 × 333 + 133 × 339)

= 0.8505

P

=

n

P

i=1

[x

C(Y )

]

=

(147 × 7 + 105 × 33 + 7 × 92 + 6 × 131)

= 0.0515

RP = P

− P

= 0.8505 − 0.0515 = 0.799

This is a measure which reflects the systematic difference with regard to the occurrence of bodily pain before and after the operation.

The content in table 12 can be graphically displayed by means of a ROC- curve given in figure 13 where the horizontal axis gives the cumulative fre- quencies for pre-operation values and the vertical axis corresponding the post-operation value.

Table 12 The pattern of change of Question 7 in SF-36 in subpopulation 3 before and after the operation; cell frequencies, marginal frequencies and the cumulative frequencies.

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 23

Figure 13 The ROC of question 7

If the two marginal distributions had been identical, the curve would have coincided with the positive diagonal, representing no effect between pre- operation and post-operation. If the curve lies above the diagonal, RP is positive, indicating that the results are better after the operation and vise versa if RP is negative. The maximum effect of RP is represented by a curve which reaches the left hand corner of the diagram. In fact, it is easy to show by means of the elementary geometry that the area of the ROC curve (be- tween the curve and the diagonal) is directly related to RP.

3.3 The difference of differences

Besides the investigation of the systematic change in one group, it is informa-

tive to study whether these systematic changes are different or not between

some particular subgroups, which are defined by two types of remission: pri-

vate and non-private here. In Question 7, we are interested to know if the

systematic change of patients’ bodily pain is the same for private patients

and non-private patients.

Figure 14 The relative operating characteristic (ROC) curves of the private patients and non-private patients

Supposing RP

and RP

are the values of RP for the private group and non- private group respectively, all values of RP

and RP

for 36 questions can be calculated in a similar way as before. The two ROC curves of 7) are shown in figure 14. With the null hypothesis ∆RP = RP

− RP

= 0, the hypothesis test can be performed. The problem is what the distribution of ∆RP looks like. We have used bootstrap simulations to see how ∆RP behaves. We used the sample size of 1000 to warrant the accuracy of unknown distributions. It appeared to be nicely normally distributed.

Figure 15 gives the confidence intervals of the different RP between before

and after operation for private and non-private in subpopulation 3. The fig-

ure shows that the differences of private and non-private patients roughly

follow the same pattern. Because the different formulation of the questions,

the confidence intervals are to be found on both side of zero.

3 PATIENTS’ ATTITUDES IN SUBPOPULATION 3 25

Figure 15 The confidence interval of RP for private and non-private

Even if there was very similar patterns for non-private and private patients, we will study in detail whether there are significant differences between pri- vate and non-private patients for some special items.

Thus we calculate the confidence interval from the bootstrap simulation.

Under the assumption that:

H

:∆RP = 0 against H

:∆RP 6= 0 We used the test variable:

Z = √

var(RPp−RPn)

= √

var(RPp)+var(RPn)

The null hypothesis H

will be rejected if |Z| > 1.96 and we then conclude that there is a difference of RP between private patients and non-private patients.

The 95% C.I can be obtained from (RP

− RP

) ± 1.96 × pvar(RP

− RP

)

As a result, we get (RP

− RP

) = 0.1237 and pvar(RP

− RP

) = 0.0575

for question 7. Therefore, the confidence interval is (0.011,0.236) which shows

that the difference with regard to bodily pain during the past four weeks is

significant.

4 Conclusions

4.1 Conclusions for all three subpopulations

Concerning the questionnaire of all three subpopulations, we conclude:

1. There are more males than females among the patients in general. There are also more males among the non-private patients than among the private patients.

2. Among the private patients, lumbar pain was somewhat less common.

However, the difference between the private and non-private patients is not statistically significant.

3. The private patients had shorter symptoms duration. The differences are not statistically significant in subpopulation 1 and subpopulation 2. However, the difference between private and non-private patients is highly significant in subpopulation 3.

4. The difference concerning sick leave between private and non-private pa- tients is negligible.

5. Among the non-private patients, physical work was a little more common.

The difference was not statistically significant however.

4.2 Conclusions for subpopulations 3

We apply the same procedure as above to get the RP differences of all 36

questions in SF-36 of subpopulation 3. Then we can get figure 16 which gives

the confidence interval of the difference between private and non-private pa-

tients.

4 CONCLUSIONS 27

Figure 16 The difference of confidence interval of RP between private and non-private

1. From figure 16, it can be seen that most of the differences between private and non-private patients are not statistically significant.

2. When using 95% confidence level for each of the 36 items, we can expect 36 × 0.05 = 1.8 or about 2 significant results due to random variation. How- ever we got 6 intervals which did not cover the point 0.

3. These questions are given in table 13 and it is worth noticing that they are all concerned with the physical health. This is in conformity with the results already given in table 9 where a significant result was found for the summary score concerning physical health only.

4. From the ROC curves figures in appendix E, we can see that even if these

differences are statistically significant, they seem to be of quite minor impor-

tance.

Table 13 The questions of significant difference RPs between private and non-private patients in subpopulation 3

No. of the question Question

3g Does your health now limit

you in walking more than one mile 4c During the past 4 weeks, were you

limited in the kind of work or other activities 4d During the past 4 weeks, do you

had difficulty performing the work or other activities 7 How much bodily pain have you

had during the past 4 weeks 8 During the past 4 weeks, how much

did pain interfere with your normal work 11d I think my health is excellent

References

[1] http://www.sf-36.org

[2] http://en.wikipedia.org/wiki/SF-36

[3] Douglas G. Altman, 1991. Practical Statistics for Medical Research, Chap- man and Hall, 236-238.

[4] Svensson, E. & Starmark, J-E., 2002. Evaluation of individual and group changes in social outcome after aneurysmal subarachnoid haemorrhage: a long-term follow-up study. Rehabil Med, 2002; 34: 251-9

[5] Svensson, E. & Sonn, U., 1997. Measures of individual and group changes in ordered categorical data: application to the ADL staircase. Scand J Rehab Med, 29, 233-242.

[6] Svensson, E., 1993. Analysis of systematic and random differences between

paired ordinal categorical data. Thesis, Department of Statistics, Chalmers

Tekniska H¨ ogskolan, G¨ oteborg University, G¨ oteborg.

4 CONCLUSIONS 29

[7] Str¨ omqvist, B, et al, 2006.Uppf¨ oljning av l¨ andryggskirurgi i Sverige. Rap- port 2006. F¨ or Svensk Ryggkirurgisk F¨ orening.

[8] Zhao, X. & Zhu, Y., 2009. Rank-based statistical methods for paired ordi- nal data. Master thesis, ¨ Obrebro University, ¨ Orebro

Acknowledgements

First and foremost I greatly appreciate my supervisor, Professor Adam Taube,

who let me deeply understand the statistics. Your enthusiasm, humor and

erudition have been invaluable to this thesis. I am also indebted to Dr. Bo

Nystr¨ om. Thank you for providing the data and giving many valuable com-

ments from medical background and disc herniation operation. Thanks to

Birgitta Gregebo, Birgitta Schillberg and other colleagues at CSS for your

arduous collecting and disposal the data.

Appendix

A Guideline to the figures

At the very beginning, we have to point out that the figures in section 2 are not the same as the ROC curves in Svensson’s method. The figures are used only for illustrating the situation in section 2.

We will give a simple example here for understanding the figures. The table 1 and figure 1 given below are the pedagogical example for illustrating the figures of ordinal data in this thesis.

Figure 1 shows the proportions in table 1 and table 2 with a similar answer options as in section 2. Then seen from figure 2, for the private patients, we plot the percentage of non-private patients as the x value of the option point in the coordinates while the percentage of private patients as the y value of the point. As a result, the dotted curve stands for the subpopulation. The area between dotted curve and diagonal reflects the difference between pri- vate and non-private patients.

The ordering of data is from the best to the worst in the figures. Therefore, if the curve is above the diagonal, there are more private patient who chose the best recovery option of the question than non-private patients. As a result, the private patients recovered better than non-private patients.

Table 1 The example table Yes Perhaps No Non-private 20% 20% 60%

private 60% 20% 20%

Table 2 The example cumulative frequency table Option 1 Option 2 Option 3

Non-private 20% 40% 100%

private 60% 80% 100%

A GUIDELINE TO THE FIGURES 31

Figure 1 The example figure in section 2

Figure 2 The example curve in section 2

B Details of questionnaires in the subpopu- lations

Table A The background table of population variables

The variable Question in the questionnaire Response

Before the operation

Age Age at OP In years

Duration Duration of symptoms In months

Gender Gender 1.Male 2.Female

DH reason How did you get your DH? 1.Related to a special event 2.Not related to anything Lumbar pain Have you had lumbar pain before

your disk herniation ?

1.No 3.Yes, long time before Physical work How much physical work was related

to your job before you had the OP?

1.Very physical 2.Not too much 3.Easy

Sick leave1 Have you been on sick leave because of your DH before the OP?

1.Yes, Fulltime sick leave 2.Yes, part-time sick leave 3.No sick leave

Sick leave2 Have you had sickleave just before the OP because of something else?

1.Yes 2.No Smoke Did you take any nicotine before your DH OP? 1. Yes 2.No

After the operation

Back pain If you had pain in the back before the OP,how did it developed after OP?

1.Disappeared to 6.Much worse

Finding 1.Sequester

2.Disk bulging 3.Other 4.No pathology Leg pain

If you had a loss of power in leg before OP, how did this developed after OP?

1.Disappeared 6.Much worse

Re Op Following OP 1.No 2. during the hospital stay

3. 3 months 4. 4-12 months 5.

≥ 1 year 6. other

B DETAILS OF QUESTIONNAIRES IN THE SUBPOPULATIONS 33

Table B The further variables for subpopulation 1

Table C The further variables for subpopulation 2

B DETAILS OF QUESTIONNAIRES IN THE SUBPOPULATIONS 35

Table D The further variables for subpopulation 3

C The SF-36 questionnaire

C THE SF-36 QUESTIONNAIRE 37

C THE SF-36 QUESTIONNAIRE 39

D The missing response rate of SF-36

No Non-pri (Before) Non-pri (After) Pri (Before) Pri (After)

1 9.28% 10.05% 10.64% 11.7%

2 2.84% 5.41% 1.06% 6.38%

3a 8.76% 9.28% 10.64% 10.64%

3b 2.84% 4.64% 1.06% 4.26%

3c 9.02% 9.28% 10.64% 10.64%

3d 5.41% 4.64% 6.38% 4.26%

3e 9.02% 9.54% 11.7% 10.64%

3f 4.9% 2.32% 6.38% 2.13%

3g 9.28% 11.34% 10.64% 10.64%

3h 5.15% 3.87% 5.32% 3.19%

3i 9.54% 9.54% 10.64% 10.64%

3j 4.9% 2.58% 5.32% 1.06%

4a 9.28% 9.79% 12.77% 10.64%

4b 4.9% 2.58% 5.32% 2.13%

4c 9.54% 10.05% 10.64% 10.64%

4d 5.15% 3.09% 7.45% 1.06%

5a 9.28% 10.05% 11.7% 10.64%

5b 5.41% 2.58% 5.32% 1.06%

5c 9.54% 9.79% 12.77% 10.64%

6 5.15% 3.09% 5.32% 1.06%

7 9.79% 11.34% 11.7% 10.64%

8 5.41% 2.32% 6.38% 1.06%

9a 9.54% 10.05% 10.64% 10.64%

9b 4.9% 2.84% 5.32% 1.06%

9c 10.57% 9.79% 10.64% 10.64%

9d 4.64% 2.58% 5.32% 1.06%

9e 9.79% 9.28% 11.7% 13.83%

9f 4.9% 2.58% 4.26% 1.06%

9g 9.79% 10.05% 10.64% 11.7%

9h 4.9% 3.09% 4.26% 1.06%

9i 10.05% 10.05% 10.64% 11.7%

10 4.9% 3.61% 4.26% 1.06%

11a 10.57% 10.05% 10.64% 11.7%

11b 4.64% 3.09% 4.26% 1.06%

11c 10.05% 11.34% 10.64% 12.77%

11d 4.09% 3.09% 4.26% 1.06%

E THE ROC CURVES OF PATIENTS’ ATTITUDES IN SUBPOPULATION 341

E The ROC curves of patients’ attitudes in

subpopulation 3

E THE ROC CURVES OF PATIENTS’ ATTITUDES IN SUBPOPULATION 343

E THE ROC CURVES OF PATIENTS’ ATTITUDES IN SUBPOPULATION 345